Find the product of the top left number and the bottom left in this box.

Do the same with the top right and bottom left numbers.

Calculate the difference between these products.

Investigate further.

The first thing I did was follow these instructions. Then I changed the box size and looked for patterns.

A two by two box…

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12×23=276 286-276= 10

13×22=286

I tested a two by two box two more times to ensure each time I got the answer of 10, also to ensure that the answer was the same in different areas of the grid. I will do this for each different size boxes.

Formula 2. 10 (n-1) for squares such as 3 X 2, 4 X 2 etc... Will it be 7 (n-1) for a 3 X 2 square in a 7 wide grid? Formula 3. 10 (n-1)(d-1) Will this be 7 (n-1)(d-1) for random boxes in a 7 wide grid? Let's see...

the amount of G's needed in the bottom two corners of a cutout. The height of the cutout takeaway 1 defines the amount of G's needed in the bottom two corners, and since this is a trend for all the different size cutouts I can now substitute this number with an algebraic expression.

Chapter Four So I have now investigated squares and rectangles in a 10x10 number grid and squares in a new 12x12 number grid. With my new 12x12 grid I have noticed my results are all multiples of 12. I am now going to repeat my processes from chapter two, except

a a+3 a+30 a+33 In my investigation I have to find the difference between, the product of the top left number and the bottom right number, and the product of the top right number and the bottom left number. So therefore I will multiply 'a' by 'a+33' and also I will multiply 'a+3' by 'a+30' and find the difference.

Nevertheless using the annotated notes on the formula my formula would look like this now: > 6N =6n x 1= 6 > 6+b=54 Now I would need to find the value of b in order to use my formula in future calculations.